Question

A fridge has a listed price of Rs. 16000. Successive discounts of 10 % and 20 % are given on its listed price. Sales tax is then charged at 30 %. Ravi bought it for Rs. S which includes sales tax. Find S.

Answer 1

Hint: We will apply the formula of finding a discount which is given by the price of the sales after discount which is equal to original price reduced by the amount in which the original amount is multiplied by the discount percentage. Numerically, this formula can be written as,
$S.P.=C.P.-\left( discount\% \right)C.P.$ where C.P. is the cost price and S.P. is the selling price. Here, the original price is the same as the cost price.

Complete step-by-step answer:
According to the question the price of the fridge is priced at Rs 16000. This will be considered as a cost price here. Now the first discount is given as 10 %. So the new price is given by the formula $S.P.=C.P.-\left( discount\% \right)C.P.$ where C.P. is the cost price and S.P. is the selling price. Here, the original price is the same as the cost price. In the 10 % discount rate we will consider C.P. as 16000 and discount as 10 %. Therefore we have
$\begin{align}
  & S.P{{.}_{1}}=C.P.-\left( discount\% \right)C.P. \\
 & \Rightarrow S.P{{.}_{1}}=16000-\left( 10\% \right)16000 \\
 & \Rightarrow S.P{{.}_{1}}=16000-\left( \dfrac{10}{100} \right)16000 \\
 & \Rightarrow S.P{{.}_{1}}=16000-1600 \\
 & \Rightarrow S.P{{.}_{1}}=14400 \\
\end{align}$
Therefore, we have the amount after 10 % discount given as Rs. 14400. Since, we have a second discount on the new selling price of Rs.14400. So we will apply the same formula of discount on the discount of 20 % on the item. Thus, we have
$\begin{align}
  & S.P{{.}_{2}}=C.P.-\left( discount\% \right)C.P. \\
 & \Rightarrow S.P{{.}_{2}}=14400-\left( 20\% \right)14400 \\
 & \Rightarrow S.P{{.}_{2}}=14400-\left( \dfrac{20}{100} \right)14400 \\
 & \Rightarrow S.P{{.}_{2}}=14400-2880 \\
 & \Rightarrow S.P{{.}_{2}}=11520 \\
\end{align}$
Therefore, we have a new selling price as Rs. 11520. Now, by the question we see a sales tax percentage given as 30 %. This sales tax needs to be multiplied to $S.P{{.}_{2}}$. Therefore, we will have the amount of sales tax = $11520\times \dfrac{30}{100}$. This is called 30 % of the amount of Rs. 11520. Thus, we have the amount of sales tax as Rs. 3456 after simplifying it. Now, we will have the amount or selling price of the fridge after the two discounts of 10 % and 20 % along with 30 % sales tax. This is given by the following formula.
Amount of the fridge = Amount of the fridge after 10 % an 20 % discounts + Amount of the fridge after a sales tax of 30 %. Therefore, Amount of the fridge = Rs. 11520 + Rs. 3456
Or, Amount of the fridge = Rs. 14976
Hence, the required amount of the fridge is given by Rs. 14976.

Note: We could have found out the price of the fridge directly by the formula for the price of any object with discounts more than one. This is an alternate method and it is done as,
Price of the fridge after deducting the discounts = $16000\left( 1-\dfrac{10}{100} \right)\left( 1-\dfrac{20}{100} \right)$.